3D Rotation

3D Rotation in Computer Graphics:
In Computer graphics, 3D Rotation is a process of rotating an object with respect to an angle in a three dimensional plane.
Consider a point object O has to be rotated from one angle to another in a 3D plane.
Let-

• Initial coordinates of the object O = (X_old, Y_old, Z_old)
• Initial angle of the object O with respect to origin = Φ
• Rotation angle = θ
• New co-ordinates of the object O after rotation = (X_new, Y_new, Z_new)

In 3 dimensions, there are 3 possible types of rotation:

• X-axis Rotation
• Y-axis Rotation
• Z-axis Rotation

For X-Axis Rotation:

This rotation is achieved by using the following rotation equations-

• X_new = X_old
• Ynew = Yold x cosθ – Zold x sinθ
• Z_new = Y_old x sinθ + Z_old x cosθ
  

In Matrix form, the above rotation equations may be represented as,

For Y-Axis Rotation:

This rotation is achieved by using the following rotation equations-

• X_new = Z_old x sinθ + X_old x cosθ
• Y_new = Y_old
• Z_new = Y_old x cosθ – X_old x sinθ

In Matrix form, the above rotation equations may be represented as-

For Z-Axis Rotation:

This rotation is achieved by using the following rotation equations-

• X_new = X_old x cosθ – Y_old x sinθ
• Y_new = X_old x sinθ + Y_old x cosθ
• Z_new = Z_old
  

In Matrix form, the above rotation equations may be represented as-